Ben is 3 times as old as Christopher. Eight years ago, Ben was 5 times as old as Christopher. How old is Ben now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Christopher. Let Ben's current age be $b$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $b = 3c$ Eight years ago, Ben was $b - 8$ years old, and Christopher was $c - 8$ years old. The information in the second sentence can be expressed in the following equation: $b - 8 = 5(c - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = b / 3$ . Substituting this into our second equation, we get: $b - 8 = 5($ $(b / 3)$ $- 8)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 8 = \dfrac{5}{3} b - 40$ Solving for $b$ , we get: $\dfrac{2}{3} b = 32$ $b = \dfrac{3}{2} \cdot 32 = 48$.